Phase function simulation in tissue phantoms: a fractal approach

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Abstract
Artificial media are needed for the calibration of optical diagnostic methods in order to work on reproducible, stable and well known samples. Since the scattering and absorption coefficients can easily be adjusted by using appropriate concentrations of scattering and absorbing components, the most difficult part in the design of a good tissue phantom is to obtain an actual phase function. The most common way to create phantoms is to use scattering microspheres of equal size, but the Mie phase function of such a phantom does not match the tissue's real phase function. Moreover, we show in this paper that the similarity relations often used for the analysis of the results obtained with this type of phantom may sometimes be very inaccurate. The use of a mixture of different sized scattering particles is then considered, in order to imitate the whole phase function. However, as the determination of adequate sizes and concentrations is a difficult mathematical task, we describe a simple method to solve this problem. We first demonstrate that the extreme optical complexity of real biological samples could be simulated by a mixture of spheres with a fractal diameter distribution. Then, we present a few simple rules based on the knowledge of this fractal distribution, which can be used to obtain a realistic phase function with a limited number of sphere diameters.